Nature of the singularity in a spin-glass model

Abstract

High temperature series expansions are developed for the specific heat of a random bond Ising model of a spin glass for standard two- and three-dimensional lattices. Pade approximant analysis of the series indicates the absence of any singularity on the positive real axis. The solution for the Bethe lattice is investigated using results obtained previously for the Mattis random site model. It is concluded that the high temperature partition function and all its derivatives with respect to magnetic field have no singularity at the transition temperature. This behaviour may also extend to lattice models.